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Two-spinor Formulation of First Order Gravity coupled to Dirac Fields

Marco Godina·Paolo Matteucci·Lorenzo Fatibene·Mauro Francaviglia
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Abstract

Two-spinor formalism for Einstein Lagrangian is developed. The gravitational field is regarded as a composite object derived from soldering forms. Our formalism is geometrically and globally well-defined and may be used in virtually any 4m-dimensional manifold with arbitrary signature as well as without any stringent topological requirement on space-time, such as parallelizability. Interactions and feedbacks between gravity and spinor fields are considered. As is well known, the Hilbert-Einstein Lagrangian is second order also when expressed in terms of soldering forms. A covariant splitting is then analysed leading to a first order Lagrangian which is recognized to play a fundamental role in the theory of conserved quantities. The splitting and thence the first order Lagrangian depend on a reference spin connection which is physically interpreted as setting the zero level for conserved quantities. A complete and detailed treatment of conserved quantities is then presented.

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Marco Godina, Paolo Matteucci, Lorenzo Fatibene, Mauro Francaviglia. 1999-03-05. Two-spinor Formulation of First Order Gravity coupled to Dirac Fields. https://doi.org/10.1023/a%3A1001804718086

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